package com.hyb.algorithm.data.struct.dp;

/**
 * 64. 最小路径和
 * https://leetcode.cn/problems/minimum-path-sum/
 * 给定一个包含非负整数的 m x n 网格 grid ，请找出一条从左上角到右下角的路径，使得路径上的数字总和为最小。
 * <p>
 * 说明：每次只能向下或者向右移动一步。
 *
 * @author: ybhu
 * @create: 2024/01/03 14:36
 */
public class MinPathSum {

    public static void main(String[] args) {
        int[][] grid = {{1, 3, 1}, {1, 5, 1}, {4, 2, 1}};

        System.out.println(new MinPathSum().minPathSum(grid));
    }

    public int minPathSum(int[][] grid) {

        int row = grid.length;
        int col = grid[0].length;

        int[][] dp = new int[row][col];

        //行处理
        dp[0][0] = grid[0][0];
        for (int i = 1; i < row; i++) {
            dp[i][0] =dp[i-1][0]+ grid[i][0];
        }

        //列处理
        for (int j = 1; j < col; j++) {
            dp[0][j] =dp[0][j-1]+ grid[0][j];
        }

        for (int i = 1; i < row; i++) {
            for (int j = 1; j < col; j++) {
                dp[i][j] = Math.min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];
            }
        }


        //最右下角
        int res=dp[row-1][col-1];
        return res;
    }
}
